PAC-Bayesian High Dimensional Bipartite Ranking

TL;DR

This paper introduces a PAC-Bayesian method for high-dimensional bipartite ranking, providing non-asymptotic risk bounds and an MCMC algorithm, demonstrating optimality and effectiveness on datasets.

Contribution

It develops a novel PAC-Bayesian approach for nonlinear additive scoring functions in high dimensions, with theoretical guarantees and practical implementation.

Findings

Risk bounds under sparsity and margin conditions

Oracle inequalities demonstrating performance

Algorithm tested on synthetic and real datasets

Abstract

This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive scoring functions, and we derive non-asymptotic risk bounds under a sparsity assumption. In particular, oracle inequalities in probability holding under a margin condition assess the performance of our procedure, and prove its minimax optimality. An MCMC-flavored algorithm is proposed to implement our method, along with its behavior on synthetic and real-life datasets.